Optical Lens with Halo Reduction

ABSTRACT

A method is provided for use in reducing a size of halo effect in an ophthalmic lens. The method comprises: providing data indicative of a given ophthalmic lens with a first pattern providing prescribed vision improvement, processing said data indicative of the features of the first pattern and generating data indicative of a variation of at least one feature of the first pattern resulting in a second pattern which maintains said prescribed vision improvement and reduces a size of halo effect as compared to that of the lens with the first pattern.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.14/367,389, filed Jun. 20, 2014, which is the National Phase applicationof International Application No. PCT/IL2012/050538, filed Dec. 20, 2012,which claims benefit to U.S. Provisional Application No. 61/578,401,filed Dec. 21, 2011, which designates the United States and waspublished in English. These applications, in their entirety, areincorporated herein by reference.

TECHNOLOGICAL FIELD AND BACKGROUND

The present invention is generally in the field of ophthalmic lenses,including contact lenses and intraocular lenses, and relates to suchlenses with reduced halo effects.

Halo effects are known as a glow or color light pattern that can be bestobserved when looking at a bright source in front of a dark background,for example a broad spot of light seen around a street light in thedark. This optical phenomenon is mainly caused by interaction of lightwith matter, and is enhanced due to diffraction of light wheninteracting with the eye, e.g. passing through the eye pupil, eyetissue, or any other diffraction of light caused by sharp edges orartificial diffraction structures, such as intraocular lens.

Techniques aimed at reducing the halo effects in lenses have beendeveloped. For example, U.S. Pat. No. 6,557,998 discloses ophthalmiclenses, for example, intraocular lenses, contact lenses, corneal implantlenses and the like, having multifocal characteristics which providebeneficial reductions in at least the perception of one or more nighttime visual symptoms such as “halos”, and “glare or flare”. According tothis technique, an intraocular lens having a baseline diopter power forfar vision correction, has a near zone including an inner region havinga substantially constant vision correction power greater than thebaseline diopter power, and an additional near zone located outwardly ofthe near zone and having vision correction powers greater than thebaseline diopter power and the near zone, and including a centralplateau region having an inner end and an outer end and visioncorrection powers which increase progressively from the inner end to theouter end.

GENERAL DESCRIPTION

The present invention provides a novel configuration of an ophthalmiclens, as well as a method of designing such lens, which, on the onehand, maintains the patient's prescribed vision improvement and, on theother hand, reduces a size of halo effect.

The present invention is in particular useful for improving lenseshaving certain pattern (first pattern) corresponding to the patient'sprescribed vision improvement, for example a pattern aimed at extendingthe depth of focus (EDOF) of an ophthalmic lens such as to enable thelens to improve both the near and far visions of a patient, rather thanusing a bi-focal or multi-focal lens. Such a first pattern is typicallyto be produced on the lens surface in a surface relief in the form of anarray of protrusions-and-pits. Generally, however, it is phase patternformed by spaced-apart regions of different optical properties, whichalternatively to the protrusions-and-pits pattern may be in the form ofspaced-apart regions of different refractive index materials, e.g. byembedding a different material into the spaced-apart surface regions ofthe lens.

According to the invention, data indicative of the features of suchfirst pattern for a given lens is used for determining variation(s) ofat least one feature of the first pattern resulting in a second pattern,which maintains the prescribed vision improvement and reduces a size ofhalo effect as compared to that of the lens with the first pattern.Then, the lens surface can be processed to form said second patternthereon.

The first pattern is typically a periodic pattern. The second patternmay be periodic or not. The at least one feature of the first patternthat is altered/varied may include one or more of the following: widthand/or depth of spaced-apart features, period, pitch, local transition(e.g. smoothness and slope at an interface between regions of differentoptical properties, such as location of slope variation or interfacebetween regions generating different phases), local slope/curvature, aswell as any other feature of the type affecting the periodicity of thefirst pattern. As indicated above, the first pattern may be configuredas EDOF pattern. This may be a substantially non-diffractive phasepattern (i.e. the pattern features are arranged on the lens surface withlow spatial frequency with regard to wavelengths of visual spectrum),for example as described in the following patent publications U.S. Pat.No. 7,061,693, WO 12/085917, U.S. Pat. No. 8,169,716, 7,812,295, allassigned to the assignee of the present application.

The present invention is based on the inventors' understanding of thefollowing: The ability of the human eye to observe the halo pattern isdue to the logarithmic response of the human eye. Light passage througha periodic structure, and in particular a periodic phase structure,typically results in certain interference/diffraction pattern such ascolor rings structure on the imaging plane, which is typically ofrelatively low intensity. Due to the fact that the human eye haslogarithmic response to light, when observing a light source over darkbackground (e.g. looking at a street light at night), suchinterference/diffraction pattern is seen as a halo effect around thelight source. Considering the phase pattern as a combination of severalamplitude sinusoidal functions, where the frequency of each sinusoidalfunction is a native multiplication of the original frequency of thephase pattern, the inventors of the present invention have found that bybreaking the periodicity of the phase pattern, the pattern could nolonger be described as a summation of sinusoidal functions with the samebase frequency, but rather with different base frequencies. This willresult, with the proper parameters of the combined pattern, inelimination of the arc color rings. The proper selection of the patternparameters (second pattern) includes altering of the feature(s) of thefirst pattern to obtain one or more of the following: (i) deviation froma local period of the first pattern; (ii) deviation from a local slopeof the first pattern (inner and outer slope); (iii) deviation from localmaximum height of protrusions in the first pattern; (iv) deviation fromlocal minimum height of protrusions in the first pattern; (v) producingadditional, typically highly dense, pattern within one type of featuresof the first pattern; and (vi) deviation from local pattern position.Also, the first pattern may be altered by producing additional,typically highly dense, pattern within one type of features of the firstpattern, e.g. within the protrusions.

The present invention provides the reduction of the size of halo effectat least by 25%.

Thus, according to one aspect of the present invention, there isprovided a method for designing an ophthalmic lens with a reduced sizeof halo effect, the method comprising:

-   -   providing data indicative of a given ophthalmic lens with a        first pattern providing prescribed vision improvement,    -   processing said data indicative of the features of the first        pattern and generating data indicative of a variation of at        least one feature of the first pattern resulting in a second        pattern which maintains said prescribed vision improvement and        reduces a size of halo effect as compared to that of the lens        with the first pattern.

Said processing of said data indicative of the features of the firstpattern may comprise estimating a halo pattern of the ophthalmic lenswith the first pattern.

According to some embodiments of the inventions said providing of thedata indicative of the ophthalmic lens with the first pattern comprisesusing data indicative of at least a dimension of an effective apertureof the lens and data indicative of prescribed vision improvement, andgenerating data indicative of features of the first pattern to beproduced on the lens to thereby provide said prescribed visionimprovement.

According to another broad aspect of the invention, there is provided anophthalmic lens comprising a surface pattern being a modification of afirst pattern which is configured for providing prescribed visionimprovement, at least one of features of said surface pattern being amodification of at least one feature of the first pattern such that saidprescribed vision improvement is maintained and a size of halo effect isreduced as compared to that of said lens with the first pattern.

According to yet another aspect of the invention, there is provided asystem for use in designing an ophthalmic lens providing prescribedvision improvement for a patient, the system comprising a control unitcomprising data input utility for receiving input data indicative of thepatient's vision and of desired vision improvement, and a processorutility for processing the input data and generating data indicative ofa surface pattern to be produced on the lens, said processingcomprising:

-   -   analyzing the input data and generating data indicative of a        first pattern to be formed on the surface of the lens to provide        desired vision improvement;    -   analyzing data indicative of the lens having said first pattern,        evaluating a size of hallo effect of the lens with the first        pattern, and generating data indicative of a change in at least        one feature of the first pattern resulting in a second pattern        which maintains said desired vision improvement and has a        reduced size of halo effect as compared to that of said lens        with the first pattern.

According to yet another aspect of the invention, there is provided asystem for use in designing an ophthalmic lens providing prescribedvision improvement for a patient, the system comprising a processorutility for receiving and processing input data indicative of a certainfirst pattern to be produced on the lens surface to provide desiredvision improvement, said processing comprising:

-   -   analyzing data indicative of the lens having said first pattern,    -   evaluating a size of hallo effect of the lens with the first        pattern, and    -   generating data indicative of a change in at least one feature        of the first pattern resulting in a second pattern which        maintains said desired vision improvement and has a reduced size        of halo effect as compared to that of said lens with the first        pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to better understand the subject matter that is disclosedherein and to exemplify how it may be carried out in practice,embodiments will now be described, by way of non-limiting example only,with reference to the accompanying drawings, in which:

FIG. 1A is a schematic illustration of a system according to theinvention for designing an ophthalmic lens;

FIG. 1B exemplifies a normalized intensity profile for a ring-likepattern producing halo effect in polychromatic illumination;

FIG. 2 is a flow chart of an example of a method of the invention fordesigning an ophthalmic lens;

FIG. 3A is a schematic illustration of an example of a lens surfaceformed with a first pattern (phase pattern) designed to provide specificvision improvement (e.g. EDOF);

FIG. 3B illustrates the analysis of the first pattern by simulating ahalo pattern induced by the lens with the first pattern of FIG. 3A;

FIG. 3C exemplifies the lens surface of FIG. 3A with the modified secondsurface pattern designed by altering the feature(s) of the first toreduce the halo pattern;

FIGS. 3D illustrates analysis of the second pattern by simulating ahallo pattern induced by the lens with the second pattern of FIG. 3C;

FIGS. 4A-4B illustrate the halo effects for the lens with the firstpattern (FIG. 3A) and lens with the second pattern (FIG. 3C) inlogarithmic intensity scale;

FIGS. 5A-5B show experimental results of measuring the intensity map oflight passing through the lens with respectively the first pattern andthe second pattern in logarithmic scale;

FIGS. 6A-6B show surface profiles of respectively a bi-focal apodizeddiffractive optical mask to be used with an optical lens and the surfaceprofile after optimization according to the invention;

FIGS. 7A-7B show halo pattern simulations corresponding to lens profilesof FIGS. 6A-6B respectively;

FIGS. 8A-8B show respectively distance MTF measurements at distance of 3mm EPD for the lens patterns of FIGS. 6A-6B;

FIGS. 9A-9B show respectively near MTF measurements at distance of 3 mmEPD for the lens patterns of FIGS. 6A-6B;

FIGS. 10A-10B show respectively near MTF measurements at distance of 4mm EPD for the lens patterns of FIGS. 6A-6B;

FIG. 11A-11B show respectively through focus MTF measurements for thelens patterns of FIGS. 6A-6B; and

FIGS. 12A-12B illustrate an example of the invention for optimizing alens with a pattern configured to provide extended depth of focus, whereFIG. 12A shows the first pattern and FIG. 12B shows an optimized secondpattern;

FIGS. 13A-13B show respective through focus MTF measurements for thefirst EDOF pattern and the second optimized pattern corresponding to thefirst and second patterns of FIGS. 12A-12B;

FIGS. 14A-14B show respective distance MTF measurements corresponding tothe first and second patterns of FIGS. 12A-12B;

FIGS. 15A-15B show respective 1.5D (intermediate) MTF measurementscorresponding to the first and second patterns of FIGS. 12A-12B;

FIGS. 16A-16B show 2.1D (Near) MTF measurements corresponding to thefirst and second patterns of FIGS. 12A-12B; and

FIGS. 17A-17B show respective halo pattern simulations corresponding tothe first and second (optimized) EDOF patterns of FIGS. 12A-12B.

DETAILED DESCRIPTION OF EMBODIMENTS

Referring to FIG. 1A, there is illustrated, by way of a block diagram, asystem 10 of the present invention configured and operable for designingan ophthalmic lens providing prescribed vision improvement for apatient. The system 10 is typically a computer system including interalia such main functional utilities as data input and output utilities12 and 14, memory utility 16, data processing and analyzing utility 18and possibly also a display 20. The system 10 is configured and operableto design, or assist in designing, ophthalmic lenses with reduced halopattern effect while providing prescribed vision improvement for variouspatients. The system 10 may receive, via the data input utility 12, dataabout prescribed vision improvement for a given ophthalmic lens of apatient (such as certain extension of depth of focus) to be used todetermine a first vision improvement pattern on the lens surface, orsuch data may include the first pattern data providing such visionimprovement. The input data is properly processed by the processingutility 18 to design such given lens which is characterized by theprescribed vision improvement and reduced halo effect. Thus, optionally,the processing utility 18 operates to first determine the first patterndata in accordance with the prescribed vision improvement, possiblyusing various recorded patterns stored in the memory utility 16. Theprocessing utility 18 includes a halo estimator module 18A whichanalyzes the lens with the first pattern and calculates theparameters/profile of halo effect resulting from the first pattern. Theprocessing utility 18 further includes a halo reduction module 18B whichoperates to analyze the halo effect of the lens with the first patternand the optical properties (features) of the first pattern (e.g.responsible for the prescribed vision improvement), identify the propervariations to be introduced to the first pattern (at least one featurethereof) to minimize the halo effect, and then generate data indicativeof a corresponding second pattern. The latter includes the modifiedfirst pattern, i.e. first pattern with the calculated variations thereofthus having minimized halo effect while maintaining the prescribedvision improvement.

This data indicative of the second pattern may then be used by amanufacturing unit 24 (patterning equipment), for producing anophthalmic lens having the second pattern. The data indicative of thesecond pattern or of a given lens with the second pattern (as the casemay be) may be stored in the memory utility 16 for later use.Additionally, various parameters of the first pattern, modificationsthereof or the second pattern may be presented to an operator via thedisplay 20 to provide control over the processing and enable humanselection of parameters.

It should be noted that considering the EDOF-based first pattern asdescribed in the above-listed patent publications U.S. Pat. No.7,061,693, WO 12/085917, U.S. Pat. No. 8,169,716, 7,812,295 assigned tothe assignee of the present application, the EDOF pattern parameters maypractically be defined only by the physical dimension of the lens, i.e.its effective aperture, and thus being more or less universal for lenseswith different optical powers, or optical power distributions. In suchcases, where the first pattern(s) can be well defined for given lenses,the present invention provides for creating a database including dataabout various lenses for prescribed improved vision together with thedata about corresponding second patterns (modified first pattern).

As indicated above, the intensity pattern of the halo effect is ordersof magnitude weaker than the illumination intensity peak. However, thehuman eye has unique nature in response to light, relative to industriallight detectors, and provides logarithmic response. The presentinvention enables simulating of a halo pattern as observed by the humaneye. To generate such a simulated halo pattern, the processing utility18 may be configured (preprogrammed) to model the photopic response of ahuman eye with a set of at least 3 wavelengths covering the visiblespectrum and appropriately adjusted and with appropriate relativeweights. Typically, the wavelengths are selected to emphasize the peakin human vision spectrum, i.e. selection of the wavelengths may becentered around a primary wavelength of 540 nm. It should be noted thatthe model may be smoother and more reliable if it is based on a highernumber of wavelengths or wavelength ranges; typically the use of 7different wavelengths may provide sufficient result.

In order to facilitate calculations, the processing utility maygenerate, or access from the memory utility 16, a look up tableincluding relations between the modeled wavelengths and RGB spectrum.Table 1 below exemplifies such wavelength to RGB ratio look up table,illustrating relative weights of certain wavelengths in the primary RGBcolors. The RGB look up table data may be transformed and normalized tocount for the modeled photopic spectrum. This is typically needed toprovide a reliable and meaningful display of the simulated results onthe display 20.

TABLE 1 λ(μm) w(weight) C_(R) C_(G) C_(B) 0.463 0.1574 0 133 255 0.4880.1539 0 250 255 0.513 0.4903 15 255 0 0.538 1 106 255 0 0.5630 0.8122197 255 0 0.588 0.3263 255 220 0 0.613 0.0570 255 122 0

The processing utility may produce a high dynamic range PSF (PointSpread Function) for each of the modeled wavelengths. The PSF isconfigured in accordance with passage of light of the associatedwavelength through a lens having a certain surface pattern.

A polychromatic halo effect is calculated by summation of all PSFscalculated for different wavelengths into RGB PSF matrices, eachcorresponding to a single color (Red, Green or Blue). The RGB PSFmatrices may be calculated by weighting and translating the properwavelengths' PSF in accordance with the wavelength-to-RGB look up table,for example in accordance with equations 1-3 below:

$\begin{matrix}{{{linear}\mspace{14mu} {psf}} = {\sum_{i}{w_{i}*{{psf}\left( \lambda_{i} \right)}}}} & \left( {{equation}\mspace{14mu} 1} \right) \\\begin{matrix}{{{linear}\mspace{14mu} {psf}} = {\sum_{i}{{psf}\left( {Color}_{i} \right)}}} \\{= {{{psf}({red})} + {{psf}({Green})} + {{psf}({Blue})}}}\end{matrix} & \left( {{equation}\mspace{14mu} 2} \right) \\{{{psf}\left( {Color}_{i} \right)} = \frac{\sum_{j}{w_{j}*{C_{i}\left( \lambda_{j} \right)}*{{psf}\left( \lambda_{j} \right)}}}{\sum_{k}{C_{i}\left( \lambda_{k} \right)}}} & \left( {{equation}\mspace{14mu} 3} \right)\end{matrix}$

Here w_(i) corresponds to the weight of wavelength λ_(i) in thespectrum, and the parameters C_(i)(λ_(j)) correspond to theRed/Green/Blue coefficients for wavelength λ_(j) as shown e.g. in lookup table 1. To simulate the logarithmic response of the human eye theprocessing utility may operate to calculate a logarithmic scale of thecombined PSF:

Log psf=log₁₀(linear psf)   (equation 4)

An appropriate cutoff threshold may be applied to the logarithmic PSF,as well as root square or similar modification to intensify the lowintensities and scale the logarithmic PSF into a linear desired rangeappropriate for display and calculations, e.g. standard RGB range ([0,1]or [0,255]). The resulting pattern provides a simulated halo effect asseen by a human eye using a given ophthalmic lens having said surfacepattern. Results of such simulation can be displayed via the displayunit 20 to provide comprehensible indication on the size of the halopattern/effect and required/desired reduction thereof.

As indicated above, a periodic phase structure may cause color ringsstructure on the imaging plane when imaging a small light source over arelatively dark background. This color rings structure, although havingvery low intensity relative to the bright light source, generates anoticeable halo pattern when viewed in a logarithmic scale (e.g. whenthe imaging plane is the retina of a human eye). This physicalphenomenon can be easily explained by describing the phase structure ofthe lens as a thin sinusoidal phase pattern at the aperture, andtransforming it to describe a point spread function (PSF) at the imagingplane by using the Fraunhofer approximation. The amplitude transmittancefunction describing a fast finite sinusoidal phase structure in theaperture may be described as:

$\begin{matrix}{{t_{A}\left( {\xi,\eta} \right)} = {{\exp \left\lbrack {j\; \frac{m}{2}{\sin \left( {2\pi \; f_{0}\xi} \right)}} \right\rbrack}{{rect}\left( \frac{\xi}{2w} \right)}{{rect}\left( \frac{\eta}{2w} \right)}}} & \left( {{equation}\mspace{14mu} 5} \right)\end{matrix}$

where f₀ is the spatial frequency of the structure, w is the aperturewidth and m represents the peak-to-peak excursion of the phase delay.The intensity pattern generated by light from a monochromatic a pointsource illumination passing through the above described phase pattern isgiven by:

$\begin{matrix}{{I\left( {x,y} \right)}\overset{\sim}{=}{\left( \frac{A}{\lambda \; z} \right)^{2}{\sum_{q = {- \infty}}^{\infty}{{J\;}_{q}^{2}\left( \frac{m}{2} \right)\sin \; {c^{2}\left\lbrack {\frac{2w}{\lambda \; z}\left( {{xqf}_{0}\lambda \; z} \right)} \right\rbrack}\sin \; {c^{2}\left( \frac{2{wy}}{\lambda \; z} \right)}}}}} & \left( {{equation}\mspace{14mu} 6} \right)\end{matrix}$

where J_(q) ² is a Bessel function of the first kind, order q, z is thedistance from the phase pattern to the imaging plane and A is theamplitude of the light. An example of intensity pattern generated on theimage plane due to light passage through the phase structure describedin equation 5 above is shown in FIG. 1B. As shown, the intensity patternincludes for a certain wavelength a set of distinct intensity peakshaving specific width and spacing resulting from periodicity of thestructure. A broadband/polychromatic illumination would sum up adisplaced intensity pattern for each wavelength. This would yield an arcof colorful rings

Reference is made to FIG. 2, showing a flow chart diagram of an exampleof the data processing method of the invention, e.g. carried out by theabove-described processing utility 18. As shown, the processing includesreceiving data indicative of the first pattern 202, this data mayinclude a structure of the first pattern and/or data about desiredvision improvement sufficient for designing said first pattern.Typically, the processing may include calculation of a polychromatic ormonochromatic point spread function (PSF) 204 associated with the firstpattern and proper imaging conditions. In order to assess size of halopattern generated by a lens having the first pattern, the processing mayinclude calculation of the halo pattern intensity 206 as describedabove. As noted, this calculation may be based on at least threewavelengths, and preferably on seven wavelengths of the visiblespectrum.

To minimize the Halo pattern the processing utility operates tocalculate variations to the first pattern 208. The variation may beaimed at altering the periodicity of the first patter, which may forexample include variations of the relative location of the differentfeatures of the first pattern 210 and/or variation of parameters of thefeatures such as the width 212 of certain features. It should be notedthat other pattern related and/or feature related parameters may be usedfor optimization of the pattern to minimize the generated halo pattern.The principles behind the variation calculation is based on theinventor's understanding that by breaking the periodicity of the phasestructure, the structure can no longer be described as a summation ofsinusoidal function with the same base frequency, but rather withdifferent base frequencies. Using the simplification of equation 6 abovewith selection of the proper parameters will result in elimination ofthe arc color rings, and reduction of the generated halo pattern. Thesecond pattern is selected as the pattern resulting from thevariation/modification of the first pattern which minimizes the halopattern. Thus, data indicative of the second pattern is generated instep 214 to be output for further use (e.g. manufacturing).

According to some embodiments of the present invention, the processingutility may operate to apply the minimizing process as follows: thefirst pattern is characterized as phase profile along the surface of thelens (or a corresponding optical element) including possible variationsof certain parameters. A halo pattern is calculated according to thefirst phase pattern, and is then minimized by variations of the selectedparameters until a minimum is selected providing the parameters for thesecond pattern.

For example, assuming a binary multi ring phase element, e.g. EDOFelement, which can be described as:

$\begin{matrix}\begin{matrix}{{g(x)} = {{\sum\limits_{n}\begin{pmatrix}{{{\exp \left( {ia}_{n} \right)}{{rect}\left( \frac{x - {n\; \Delta \; x} - {\delta \; x_{n}}}{W_{n}} \right)}} -} \\{{rect}\left( \frac{x - {n\; \Delta \; x} - {\delta \; x_{n}}}{W_{n}} \right)}\end{pmatrix}} +}} \\{{{rect}\left( \frac{x}{W_{T}} \right)}} \\{= {\left( {\sum\limits_{n}{\left( {{\exp \left( {ia}_{n} \right)} - 1} \right){{rect}\left( \frac{x - {n\; \Delta \; x} - {\delta \; x_{n}}}{W_{n}} \right)}}} \right) +}} \\{{{rect}\left( \frac{x}{W_{T}} \right)}}\end{matrix} & \left( {{equation}\mspace{14mu} 7} \right)\end{matrix}$

where W_(n) is the width of each phase groove/feature, Δx is thedistance between adjacent features and δx_(n) define variations in thelocation of each feature, i.e. the deviation of the periodicity of thepattern resulting from changes in the position of each groove/feature.The overall size of the phase pattern is W_(T) which actually describesthe full aperture of the corresponding lens/optical element. Thisnon-limiting example is based on the assumption that the phases a_(n) ofall features are equal and can thus be replaced by a₀, it should howeverbe noted that this assumption is used to simplify the analyticcalculations and the same technique may be utilized for featuresproviding different phases. Thus the first pattern may be described as:

$\begin{matrix}{{g(x)} = {\left( {\left( {{\exp \left( {ia}_{0} \right)} - 1} \right){\sum\limits_{n}{{rect}\left( \frac{x - {n\; \Delta \; x} - {\delta \; x_{n}}}{W_{n}} \right)}}} \right) + {{rect}\left( \frac{x}{W_{T}} \right)}}} & \left( {{equation}\mspace{14mu} 8} \right)\end{matrix}$

As indicated above, to calculate the halo pattern generated by imaging apoint source by an optical element carrying the first pattern (e.g.pattern of equation 8) the processing may include calculation of the PSFassociated with first phase pattern. Generally (for monochromaticillumination) the PSF can be calculated as the Fourier transform of thephase pattern providing:

$\begin{matrix}\begin{matrix}{{p(\mu)} = {\int{{g(x)}{\exp \left( {2\pi \; {ix}\; \mu} \right)}{dx}}}} \\{= {{\left( {{\exp \left( {ia}_{0} \right)} - 1} \right)\begin{pmatrix}{\sum\limits_{n}{W_{n}\sin \; {c\left( {W_{n}\mu} \right)}\exp}} \\\left( {2\pi \; i\; {\mu \left( {{n\; \Delta \; x} + {\delta \; x_{n}}} \right)}} \right)\end{pmatrix}} +}} \\{{W_{T}\sin \; {c\left( {W_{T}\mu} \right)}}}\end{matrix} & \left( {{equation}\mspace{14mu} 9} \right)\end{matrix}$

As generally known, the PSF is defined as a response of an opticalelement to illumination by a point source, i.e. the image generated on acorresponding imaging plane. Typically, the PSF, as calculated above formonochromatic illumination, describes the field generated by the pointsource and not the intensity. The intensity pattern itself for all thediffraction orders, is given by:

$\begin{matrix}{I_{Halo} = {{\sum\limits_{m}{{p\left( \frac{m}{\Delta \; x} \right)}}^{2}} = {{{{{\exp \left( {ia}_{0} \right)} - 1}}^{2}\left( {\sum\limits_{m}{{\sum\limits_{n}{W_{n}\sin \; {c\left( {W_{n}\frac{m}{\Delta \; x}} \right)}{\exp \left( {2\pi \; i\; \frac{m}{\Delta \; x}\left( {{n\; \Delta \; x} + {\delta \; x_{n}}} \right)} \right)}}}}^{2}} \right)} = {{{{{\exp \left( {ia}_{0} \right)} - 1}}^{2}{\sum\limits_{m}\left( {\left( {\sum\limits_{n}{W_{n}\sin \; {c\left( {W_{n\;}\frac{m}{\Delta \; x}} \right)}{\exp \left( {2\pi \; i\; \frac{m}{\Delta \; x}\delta \; x_{n}} \right)}}} \right) \cdot \cdot \left( {\sum\limits_{k}{W_{k}\sin \; {c\left( {W_{k}\frac{m}{\Delta \; x}} \right)}{\exp \left( {{- 2}\; \pi \; i\; \frac{m}{\Delta \; x}\delta \; x_{k}} \right)}}} \right)} \right)}} = {\sum\limits_{n}{\sum\limits_{k}\left( {\sum\limits_{m}{W_{n}W_{k}\sin \; {c\left( {W_{n}\frac{m}{\Delta \; x}} \right)}\sin \; {c\left( {W_{k}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{n}} - {\delta \; x_{k}}} \right)}}{\Delta \; x} \right)}}} \right)}}}}}} & \left( {{equation}\mspace{14mu} 10} \right)\end{matrix}$

It can be seen that the expression within the double summation, i.e.

$\sum\limits_{m}{W_{n}W_{k}\sin \; {c\left( {W_{n}\frac{m}{\Delta \; x}} \right)}\sin \; {c\left( {W_{k}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{n}} - {\delta \; x_{k}}} \right)}}{\Delta \; x} \right)}}$

can be described as a Discrete Fourier Transform (DFT) of the function:

$\begin{matrix}{{\psi_{m}\left( {n,k} \right)} \equiv {W_{n}W_{k}\sin \; {c\left( {W_{n}\frac{m}{\Delta x}} \right)}\sin \; {c\left( {W_{k}\frac{m}{\Delta x}} \right)}}} & \left( {{equation}\mspace{14mu} 11} \right)\end{matrix}$

calculated at the coordinate (δx_(n)−δx_(k)). Using this identity, theintensity of the halo pattern is given by:

$\begin{matrix}{I_{Holo} = {{\sum\limits_{n}{\sum\limits_{k}{\sum\limits_{m}{{\psi_{m}\left( {n,k} \right)}{\exp\left( \frac{2\pi i{m\left( {{\delta x_{n}} - {\delta x_{k}}} \right)}}{\Delta x} \right)}}}}} = {\sum\limits_{n}{\sum\limits_{k}{\overset{\sim}{\psi}\left( {{\delta x_{n}} - {\delta x_{k}}} \right)}}}}} & \left( {{equation}\mspace{14mu} 12} \right)\end{matrix}$

where {tilde over (Ψ)}(δx_(n)−δx_(k)) is the DFT of Ψ_(m)(n, k).

As indicated above, the processing is aimed at generating a secondpattern configured to minimize the halo pattern. It should be noted thatthe intensity field as described in equations 10-13 includes the mainillumination lobe (the image of the light source) as well as thediffraction lobes representing the halo pattern. It should also be notedthat the optimization technique of the present invention may be operatedon the full expression due to the fact that this expression presents aphysical phenomenon and that an image of the light source willphysically be maintained. This is described more specifically furtherbelow with respect to MTF simulations and measurements of the optimizedand non-optimized lenses. To this end the processing may first operateto locate a minimal halo pattern by variation of location of the phasefeatures, to simplify the calculation, the halo pattern may be describedby:

$\begin{matrix}\begin{matrix}{I_{Halo} = {{\sum\limits_{n \neq l}{\sum\limits_{k \neq l}{\overset{\sim}{\psi}\left( {{\delta \; x_{n}} - {\delta \; x_{k}}} \right)}}} + {\sum\limits_{q \neq l}{\overset{\sim}{\psi}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}} +}} \\{{{\sum\limits_{q \neq l}{\overset{\sim}{\psi}\left( {{\delta \; x_{q}} - {\delta \; x_{l}}} \right)}} + {\overset{\sim}{\psi}(0)}}} \\{= {{\sum\limits_{n \neq l}{\sum\limits_{k \neq l}{\overset{\sim}{\psi}\left( {{\delta \; x_{n}} - {\delta \; x_{k}}} \right)}}} +}} \\{{{2\; {\sum\limits_{q \neq l}{\overset{\sim}{\psi}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}} + {\overset{\sim}{\psi}(0)}}}\end{matrix} & \left( {{equation}\mspace{14mu} 13} \right)\end{matrix}$

To minimize this expression, with respect to feature locations, theprocessing includes deriving of equation 13 with respect to δx_(l) andcomparing the derivative to zero:

$\begin{matrix}{{\frac{\partial I_{Halo}}{{\partial\delta}\; x_{l}} = 0}\begin{matrix}{\frac{\partial I_{Halo}}{{\partial\delta}\; x_{l}} = {\frac{\partial}{{\partial\delta}\; x_{l}}\begin{pmatrix}{2{\sum\limits_{q \neq l}{\sum\limits_{m}{W_{l}W_{q}\sin \; {c\left( {W_{l}\frac{m}{\Delta \; x}} \right)}\sin \; c}}}} \\{\left( {W_{q}\frac{m}{\Delta \; x}} \right){\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}{\Delta \; x} \right)}}\end{pmatrix}}} \\{= {4\pi \; i{\sum\limits_{q \neq l}{\sum\limits_{m}{\frac{m}{\Delta \; x}W_{l}W_{q}\sin \; {c\left( {W_{l}\frac{m}{\Delta \; x}} \right)}}}}}} \\{{\sin \; {c\left( {W_{q}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}{\Delta \; x} \right)}}}\end{matrix}} & \left( {{equation}\mspace{14mu} 14} \right)\end{matrix}$

providing the result:

$\begin{matrix}{{\sum\limits_{m}{\sum\limits_{q \neq l}{\frac{m}{\Delta x}{\overset{\sim}{\psi}\left( {{\delta \; x_{l}}\  - {\delta x_{q}}} \right)}}}} = 0} & \left( {{equation}\mspace{14mu} 15} \right)\end{matrix}$

Thus, by varying the locations of the features of the first pattern tosatisfy equation 15, at least a local minima of the size and intensityof the halo pattern can be found.

Further, the processing may include minimization of the halo patternwith respect to width of the phase features. The processing may thusinclude calculation of the derivative of the halo pattern with respectto width of the features:

$\begin{matrix}{{\frac{\partial I_{Halo}}{\partial W_{l}} = 0}\begin{matrix}{\frac{\partial I_{Halo}}{\partial W_{l}} = {\frac{\partial}{\partial W_{l}}\begin{pmatrix}{2{\sum\limits_{q \neq l}{\sum\limits_{m}{W_{l}W_{q}\sin \; {c\left( {W_{l}\frac{m}{\Delta x}} \right)}}}}} \\{{\sin \; {c\left( {W_{q}\frac{m}{\Delta x}} \right)}{\exp\left( \frac{2\pi i{m\left( {{\delta x_{l}} - {\delta x_{q}}} \right)}}{\Delta x} \right)}} +} \\{\sum\limits_{m}{W_{l}^{2}\sin \; {c^{2}\left( {W_{l}\frac{m}{\Delta x}} \right)}}}\end{pmatrix}}} \\{= {\frac{\partial}{\partial W_{l}}\begin{pmatrix}\begin{matrix}{2{\sum\limits_{q \neq l}{\sum\limits_{m}{\frac{\Delta \; x^{2}}{\pi^{2}m^{2}}{\sin \left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}}}}} \\{{{\sin \left( {\pi \; W_{q}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}{\Delta \; x} \right)}} +}\end{matrix} \\{\sum\limits_{m}{\frac{\Delta \; x^{2}}{\pi^{2}m^{2}}{\sin^{2}\left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}}}\end{pmatrix}}} \\{= {\frac{2\Delta \; x}{\pi}{\sum\limits_{q \neq l}{\sum\limits_{m}\frac{\cos \left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}{m}}}}} \\{\begin{pmatrix}{{{\sin \left( {\pi \; W_{q}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}{\Delta \; x} \right)}} +} \\{\frac{2}{Q - 1}{\sin \left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}}\end{pmatrix}}\end{matrix}} & \left( {{equation}\mspace{14mu} 16} \right)\end{matrix}$

where Q, appearing in the last line of equation 16, is the number ofdifferent phase elements/features along the pattern, e.g. the number ofrings in the pattern exemplified in equation 7. The requirement forminimal halo size results with:

$\begin{matrix}{{\sum\limits_{q \neq l}{\sum\limits_{m}{\frac{\cos \left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}{m}\left( {{{\sin \left( {\pi \; W_{q}\frac{m}{\Delta \; x}} \right)}{\exp\left( \frac{2\pi \; {{im}\left( {{\delta \; x_{l}} - {\delta \; x_{q}}} \right)}}{\Delta \; x} \right)}} + {\frac{2}{Q - 1}{\sin \left( {\pi \; W_{l}\frac{m}{\Delta \; x}} \right)}}} \right)}}} = 0} & \left( {{equation}\mspace{14mu} 17} \right)\end{matrix}$

It should be noted that additional parameters of the pattern may bevaried to located a minimum in the halo size. It should also be notedthat according to some embodiments the minimization process includessimultaneous minimization of the halo size with respect to allparameters used, i.e. in this non-limiting example simultaneous solutionof equations 15 and 17.

The minimization process results in the identified parameter variationsproviding a second phase pattern that will provide a reduced halo sizewhen used on an optical element (e.g. ophthalmic lens). This is whilemaintaining the desired vision improvement as provided by the firstpattern. FIGS. 3A-3D illustrate an example of a first pattern (FIG. 3A)designed diffractive bi-focal lens with a 1.8 Diopter addition, a halopattern corresponding to the first pattern FP relative to that of clearaperture CA (FIG. 3B) and a second pattern, generated by minimization ofthe halo pattern as described above (FIG. 3C) and the corresponding halopattern SP (FIG. 3D).

As shown FIG. 3A shows a plot of a surface relief first pattern designedto pattern a surface of an ophthalmic lens. The first pattern shown inthis non-limiting example is designed to generate an additional powerover the original focus of the lens ophthalmic lens, in this example thepattern is designed to introduce an addition of 1.8 Diopter, to therebygenerate a bi-focal lens. FIG. 3B shows a simulated halo intensitypattern resulting from light passage through an open clear aperture CAand through a lens carrying the first pattern FP of FIG. 3A. Thesimulated halo pattern is shown as intensity of the halo (in logarithmicscale) along the vertical axis, relative to radial distance from theoptical axis in micrometers (horizontal axis). As shown, light passagethrough a lens carrying this first pattern provides halo patternintensity being relatively higher than the halo pattern resulting fromlight passage through a clear aperture.

Processing of the first pattern (shown in FIG. 3A) according to theabove described technique (i.e. introducing variations to features andto the periodicity of the first pattern to minimize halo patternintensity) generates a second pattern configured to provide the desiredvision improvement (bi-focal lens) with reduced halo effect. Such secondpattern, being a surface relief pattern to be applied on a surface of anophthalmic lens is exemplified in FIG. 3C. FIG. 3D shows a simulatedcomparison between halo pattern intensity generated from light passagethrough a clear aperture CA and through a lens carrying the secondpattern SP of FIG. 3C similar to that of FIG. 3B. As shown in thesefigures, the halo pattern intensity generated by light passage through alens having the second pattern is reduced, at least at radial distancegreater than ˜125 μm from the optical axis, relative to that of thefirst pattern. Additionally, the halo pattern intensity is reducedalmost to the level of clear aperture (i.e. aperture with no pattern atall).

FIGS. 4A and 4B show additional simulated results of the halo patterngenerated respectively due to light transmission trough a lens having afirst pattern (as shown in FIG. 3A) and a second pattern (as shown inFIG. 3C) in logarithmic scale of intensity. These simulated results aregenerated according to the halo simulation technique described above,with reference to table 1 and to equations 1-4 above. As seen in theseresults, the halo pattern is formed by plurality of rings around acentral illumination lobe with diminishing intensity. As also shown, thesecond pattern (FIG. 4B) generates reduced halo pattern, with less ringswhich are closer to the central lobe relative to the halo patterngenerated by the first pattern (FIG. 4A).

A similar effect is shown in FIGS. 5A-5B showing respectivelyexperimental halo measurement in logarithmic scale corresponding to alens with a first pattern as shown in FIG. 3A, and to a lens carrying anassociated second pattern (i.e. the pattern of FIG. 3B) generated inaccordance with the technique of the present invention. Theseexperimental results show how the halo pattern is reduced by intensityand size due to the variations of the first pattern selected to minimizeits creation.

Reference is now made to FIGS. 6A-6B showing one other example of thetechnique of the present invention. FIGS. 6A-6B illustrate surfaceprofiles of respectively a bi-focal apodized diffractive optical mask(i.e. a mask which is to be incorporated with or attached to anophthalmic lens) and the surface profile after halo pattern minimization(optimization) according to the technique of the present invention. FIG.6A exemplifies a surface relief to be patterned on a light collectingsurface of an ophthalmic lens, being configured to alter the lens'curvature at different regions thereof in order to provide the lens withbi-focal characteristics. FIG. 6B exemplifies the surface patternreceived after optimization of the halo pattern effect to minimize sizeof the halo pattern. This minimization includes variations of relativesize, location and slope of regions as well as different localtransitions configured to provide first and second optical powers of thelens. The resulting lens profile of FIG. 6B provides a substantiallysimilar bi-focal characteristic but with reduces size of halo pattern asshown below. It should be noted that the optical masks of FIGS. 6A and6B are generally configured to be associated with a lens having the sameeffective aperture. However, in order to reduce a halo pattern, theoriginal design of the mask (FIG. 6A) does not utilize the entireaperture of the lens and covers only a part of the lens. The optimizedpattern is configured to reduce the halo effect and can thus utilize alarger portion of the lens' aperture. This provides, in addition to thereduction of the halo pattern, a stronger near vision improvement effectin dark conditions, i.e. when the user's pupils are larger.

FIGS. 7A-7B, 8A-8B, 9A-9B, 10A-10B and 11A-11B show several simulationresults exemplifying the reduction of halo pattern effects as well asthe preservation of the intended vision improvement of the lens. FIGS.7A-7B show respectively simulations of halo pattern caused by light(from a relatively small light source over a dark background) throughthe lens patterns of FIG. 6A and 6B. As shown, the resulting halopattern of the optimized lens profile is reduced after optimization ofthe lens profile. FIGS. 8A-8B, 9A-9B, 10A-10B and 11A-11B showModulation Transfer Function (MTF) simulations of the lens patterns ofFIGS. 6A-6B respectively. FIGS. 8A-8B show distance (first focal point)MTF measurements at the first focal plane using 3 mm EPD, FIGS. 9A-9Bshow respectively near (the second focal point) MTF measurements at thesecond focal plane using 3 mm EPD, FIGS. 10A-10B show respectively nearMTF measurements at the second focal plane using f 4 mm EPD and FIGS.11A-11B show through focus MTF. It should be understood that the firstfocal plane of the lens is mainly used for improvement of far (distance)vision (i.e. of distant objects) and the second focal plane is mainlyused for improvement of near vision (i.e. of objects located near to theeyes). These figures demonstrate that the MTF profile of the lens issubstantially maintained after optimization of the pattern according tothe present invention. Thus, the technique of the present inventionmaintains the optical performance of the lens (as prescribed for thepatient's vision improvement) at different dimensions of the effectiveapertures of the lens while reducing the halo pattern. As shown in FIGS.11A-11B, the overall performance and additional optical power created bythe optical design of the first pattern is maintained, i.e. the lensprovides an additional focal plane corresponding to optical power of 1.8Diopter.

FIGS. 12A-12B, 13A-13B, 14A-14B, 15A-15B, 16A-16B and 17A-17Bdemonstrate the technique of the present invention when applied to anoptical element configured to extend the depth of focus of an ophthalmiclens (i.e. the first, vision improvement pattern is an EDOF pattern).FIGS. 12A-12B exemplify the optimization of the lens with EDOF phasepattern, where FIG. 12A shows the first (original) pattern and FIG. 12Bshows the second pattern optimized according to the present invention toreduce the halo effect of the lens with pattern of FIG. 12A. In thisexample, the EDOF pattern is in the form of a surface relief including afew spaced-apart concentric ring-like phase-affecting features spaced bythe lens regions, and the figures show the pattern along the radial axisof the lens.

FIGS. 13A-13B, 14A-14B, 15A-15B, 16A-16B illustrate how the optimized(second) pattern maintains the optical performance in the sense ofextended depth of focus as well as spatial frequencies, for eachdiscrete axial location. FIGS. 17A-17B show the reduction of the haloeffect in the lens with the second pattern as compared to the lens withthe first pattern. FIGS. 13A-13B show respective through focus MTFmeasurements for the first EDOF pattern and the second optimizedpattern; FIGS. 14A-14B show respective distance MTF measurements; FIGS.15A-15B show respective 1.5D (intermediate) MTF measurements; FIGS.16A-16B show 2.1D (Near) MTF measurements; and FIGS. 17A-17B showrespective halo pattern simulations corresponding to the first andsecond (optimized) EDOF patterns. As shown, the technique of the presentinvention is based on varying feature(s) of the first pattern to reducethe size of halo pattern while maintaining the optical properties whichprovide the prescribed vision improvement. As shown, other than thesignificant reduction in the size of the hallo pattern simulated inFIGS. 17A-17B, the MTF (i.e. optical properties providing the desiredvision improvement) is kept substantially similar for various spatialfrequencies at the desired locations associated with the optical powerand depth of focus provided by the lens and the associated pattern.

Thus, the present invention provides a technique suitable for design ofan ophthalmic lens configured to provide prescribed vision improvementwith reduced halo pattern. The technique may include variations to oneor more pattern and/or feature parameters of a first pattern, designedonly to provide appropriate vision improvement, to thereby generate asecond pattern maintaining the desired vision improvement whileproviding reduce halo effect. Those skilled in the art will readilyappreciate that various modifications and changes can be applied to theembodiments of the invention as hereinbefore described without departingfrom its scope defined in and by the appended claims.

1. A method for use in reducing a size of halo effect in an ophthalmiclens, the method comprising: providing data indicative of a givenophthalmic lens with a first pattern providing prescribed visionimprovement, processing said data indicative of the features of thefirst pattern and generating data indicative of a variation of at leastone feature of the first pattern resulting in a second pattern whichmaintains said prescribed vision improvement and reduces a size of haloeffect as compared to that of the lens with the first pattern.
 2. Themethod of claim 1, wherein said processing of said data indicative ofthe features of the first pattern comprises estimating a halo pattern ofthe ophthalmic lens with the first pattern.
 3. The method of claim 1,wherein said first pattern is configured for extending a depth of focusof the lens.
 4. The method of claim 3, wherein the reduction of the sizeof halo effect is at least 25%.
 5. The method of claim 1, wherein saidaltering of the at least one feature of the first pattern comprises atleast one of the following: (i) deviation from a local period of thefirst pattern; (ii) deviation from a local slope of the first pattern,the local slope being either one of inner and outer slope; (iii)deviation from local maximum height of protrusions in the first pattern;(iv) deviation from local minimum height of protrusions in the firstpattern; (v) producing additional, typically highly dense, patternwithin one type of features of the first pattern; and (vi) deviationfrom local pattern position.
 6. The method of claim 1, wherein saidfirst pattern is a periodic pattern.
 7. The method of claim 6, whereinthe second pattern is either periodic or not.
 8. The method of claim 1,wherein said providing of the data indicative of the ophthalmic lenswith the first pattern comprises using data indicative of at least adimension of an effective aperture of the lens and data indicative ofprescribed vision improvement, and generating data indicative offeatures of the first pattern to be produced on the lens to therebyprovide said prescribed vision improvement.
 9. An ophthalmic lenscomprising a surface pattern being a modification of a first patternwhich is configured for providing prescribed vision improvement, atleast one of features of said surface pattern being a modification of atleast one feature of the first pattern such that said prescribed visionimprovement is maintained and a size of halo effect is reduced ascompared to that of said lens with the first pattern.
 10. The ophthalmiclens of claim 9, wherein said first pattern is configured for extendinga depth of focus of the lens.
 11. The ophthalmic lens of claim 9,wherein the reduction of the size of halo effect is at least 25%. 12.The ophthalmic lens claim 9, wherein said modification of the at leastone altered feature comprises at least one of the following: (i)deviation from a local period of the first pattern; (ii) deviation froma local slope of the first pattern, the local slope being either one ofinner and outer slope; (iii) deviation from local maximum height ofprotrusions in the first pattern; (iv) deviation from local minimumheight of protrusions in the first pattern; (v) producing additional,typically highly dense, pattern within one type of features of the firstpattern; and (vi) deviation from local pattern position.
 13. Theophthalmic lens of claim 9, wherein said first pattern is a periodicpattern.
 14. The ophthalmic lens of claim 13, wherein said surfacepattern, being the modification of the first pattern, is either periodicor not.
 15. A system for use in designing an ophthalmic lens providingprescribed vision improvement for a patient, the system comprising acontrol unit comprising data input utility for receiving input dataindicative of the patient's vision and desired vision improvement, and aprocessor utility for processing the input data and generating dataindicative of a surface pattern to be produced on the lens, saidprocessing comprising: analyzing the input data and generating dataindicative of a first pattern to be formed on the surface of the lens toprovide desired vision improvement; analyzing data indicative of thelens having said first pattern, evaluating a size of hallo effect of thelens with the first pattern, and generating data indicative of a changein at least one feature of the first pattern resulting in a secondpattern which maintains said desired vision improvement and has areduced size of halo effect as compared to that of said lens with thefirst pattern.
 16. (canceled)